How to use
- Choose one-sample, two-sample, or paired based on your study design.
- Pick summary stats if you already know n, mean, and standard deviation, or raw data if you want this page to summarize pasted values first.
- Set the tail and confidence level, run the analysis, then read the p-value and Cohen’s d together before drawing a conclusion.
Wave 1 statistics expansion
Three t-test workflows in one page
The first release keeps the scope disciplined: one-sample, independent two-sample, and paired tests, with summary and raw inputs, confidence intervals, effect sizes, result copy, and settings-only share URLs.
Inputs
Use this mode when you compare one sample mean with a target or reference mean.
Use this mode for two independent groups. Welch is the safer default when group variances or sample sizes differ.
Use this mode for matched observations such as before/after or left/right measurements. This page defines the paired difference as after − before.
Paste one numeric sample. Spaces, commas, tabs, and line breaks all work.
Paste one independent group per box. This page summarizes both groups locally, then runs the selected two-sample t workflow.
Paste matched values in order. The page computes each paired difference as after − before.
What the page computes
- The selected input mode is summarized into sample size, mean, and standard deviation if needed.
- The page computes the t statistic, degrees of freedom, and p-value for the chosen design.
- The same run also returns a confidence interval and a standardized effect size.
Sample breakdown
Run a test to populate the descriptive summary table.
How to interpret the result
- Use the study design first: one-sample for one group versus a target, two-sample for independent groups, and paired for matched observations.
- The p-value tells you how compatible the data are with the null hypothesis. Cohen’s d tells you how large the estimated effect is on a standardized scale.
- When the two-sample page flags Welch as safer, it means unequal variances or imbalanced group sizes may make the pooled-variance version harder to justify.
- If you need z-tests, proportion tests, Wilson intervals, or a mixed workflow page, switch to the confidence interval & hypothesis test wizard.
FAQ
When should I use paired instead of two-sample?
Use a paired t-test when each observation in one condition is matched to the same subject or unit in the other condition, such as before-versus-after measurements. Use a two-sample t-test when the groups are independent.
What is the difference between this page and the CI & hypothesis test wizard?
This page stays focused on t-tests for means, adds raw data paste boxes, and shows Cohen’s d next to the p-value and confidence interval. The broader wizard covers more test families in one place.
Does the share URL include my raw data?
No. The share URL stores only lightweight settings such as the t-test mode, tail, confidence level, input type, and two-sample variance model. Entered values stay in your browser.
Why show both p-value and Cohen’s d?
The p-value tells you how unusual the result is under the null hypothesis, while Cohen’s d helps you judge the size of the effect on a standardized scale. They answer different questions and should be read together.
Should I use Welch or equal-variance two-sample t-test?
Welch is usually the safer default because it does not require equal variances. Use the equal-variance version only when that assumption is justified by the study design or prior evidence.
What to compare next
If you are still in the planning stage, start with the sample-size calculator before collecting data. If you need a more general hypothesis test workflow, move to the CI & hypothesis test wizard. If you already have a t result and want the standardized magnitude view next to the p-value, open the effect-size calculator before final interpretation.
Related calculators
Comments (optional)
To reduce load, comments are fetched only when needed.